UNIVERSITY OF MALTA
THE MATRICULATION EXAMINATION
INTERMEDIATE LEVEL
PURE MATHEMATICS
May 2014
EXAMINERS’ REPORT
MATRICULATION AND SECONDARY EDUCATION
CERTIFICATE EXAMINATIONS BOARD
IM EXAMINERS’ REPORT MAY 2014
Pure Mathematics
Intermediate Level
May 2014
Part 1: Statistical Information
The distribution of grades awarded in the May 2014 session is given in the table below.
GRADE
A
B
C
D
E
F
Abs
Number
42
64
140
124
99
183
42
% of Total
6.05
9.22
20.17
17.87
14.27
26.37
6.05
Total
694
100
Part 2: Comments regarding candidate’s performance
Q1:
Overall, the candidates did reasonably well in this question.
The candidates do not seem to realize that these are short questions which do not
require pages and pages of calculations. For instance, in part(a), instead of substituting
for x from the first equation into the second to (easily) find the value of y, most candidates
preferred to take logs without distinguishing between Natural logs and Common logs,
thus producing incorrect calculations.
Part(b): A recurring mistake from one year to another is that candidates wrongly assume
that:
log (P+Q) = log P + log Q .
A large number of solutions were completely incorrect.
Part(c) was very well attempted.
Q2:
The candidates did well in this question.
In part (a) however, same candidates used incorrect identities such as :
cos x  sin x  1
and
2sin 2 x  2 cos 2 x  1.
Some candidates found difficulties in solving the quadratic equation
2 cos 2 x  5cos x  3  0.
Part (b): The partial fractions part was very well done.
In part (c), some candidates seemingly ignored the constant of integration, whilst others
thought that

Q3:
2
dx is equal to 2 log(2 x  1) .
2x 1
The candidates generally did well in this question.
Part (a) was very well attempted. Some candidates found
u30 instead of S30 .
In part (b), some candidates did not know the formula for
S .
The last part was not very well answered. One common error was that
There were also inequalities like
n  23.24  n  24.
4
n
2 3

6n .
4
IM EXAMINERS’ REPORT MAY 2014
Q4:
This question was well answered by the candidates.
Some candidates obtained the value of x that provided the minimum value of p(x), but
then did not proceed to evaluate the minimum value of p(x).
The range of p(x) was correctly defined and the sketch of part (iii) was drawn properly by
most of the candidates.
The derivation of the equation of the tangent in part (iv) was done correctly by most
candidates.
Part (v) was also worked out correctly by nearly all the candidates who attempted it.
Q5:
In Part (a), the binomial expansion was correctly applied in part (i) by most candidates,
although the binomial coefficients were found incorrectly in some cases. The commonest
error in part (ii) was the use of an inappropriate value of x in the approximation.
In Part (b), (i) was correctly worked by most candidates, but parts (ii) and (iii) were less
satisfactory.
Q6:
Many candidates showed inadequate knowledge of the properties of a pentagon. Others
used an incorrect value for radius of the circle drawn through the vertices of the polygon,
whilst other responses suggested a poor understanding of what a proof is. This question
was generally poorly answered.
Q7:
The derivatives asked for in part (a) of this question were obtained correctly by a good
number of candidates. Most of those who answered incorrectly assumed that the
derivative of
e  x is unaltered, or simply did not apply the right differentiation rule.
Part (b) was answered wrongly by most candidates. Responses suggested that most of
them simply did not understand the question, as evidenced by an incorrect diagram.
Others could not obtain the area A( x ) even when the diagram was correct.
Q8:
Part (a) of this question was answered correctly by less than half of the candidates. Most
of them either wrongly separated the fraction of the right hand side, or else did not
integrate it correctly.
The candidates fared much better in part (b), although some candidates did not use
radian measure to evaluate the integral. Others either omitted the sketch or drew it
incorrectly.
Q9:
This was generally well answered by the candidates. Most of them managed to work out
parts (i) and (ii) of this question correctly.
In part (iii), a good number of students did not give a correct geometrical interpretation for
2
2
BA or (BA) . Some of these candidates either commented on only one of BA or (BA) ,
or simply wrote a comment that was not asked for. In particular, some students simply
IM EXAMINERS’ REPORT MAY 2014
2
said that (BA) is the identity matrix, which, while true, is not a geometrical interpretation
2
of (BA) .
Q10:
This question was generally well answered.
In part (a), most candidates found AB + 2B correctly, as were the constants a and b.
In part (b), many responses correctly identified the inverse of matrix P, whereas some
candidates evaluated the determinant of the matrix incorrectly. In (ii), however, there
-1
were quite a few candidates who incorrectly evaluated QP to obtain matrix R instead of
-1
the correct P Q .
Chairperson
2014 Examination Panel